Crystal Structure of Localized Quantum Unipotent Coordinate Category

Watch a 47-minute mathematics lecture exploring the crystal structure of localized quantum unipotent coordinate categories. Learn how for a monoidal category with a real commuting family, a localization can be defined, focusing on the quiver Hecke algebra associated with symmetrizable Kac-Moody Lie algebras. Discover how the family of self-dual simple modules in the localized quantum unipotent coordinate category holds a crystal structure and is isomorphic to cellular crystals, first demonstrated for simple Lie algebras and the longest Weyl group element, then extended to general symmetrizable Kac-Moody Lie algebras and general Weyl group elements through joint work with M. Kashiwara.